ABSTRACT
We consider the following problem https://www.w3.org/1998/Math/MathML"> { L u = f ( x , u ) u → 0 | x | → ∞ ( x ∈ I R n , n > 2 ) u > 0 , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003062271/3a9a5b62-3a88-4cc5-923a-97624426ebfd/content/math1l.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where L = —Δ + c 2, c > 0, f(x, 0) = 0, f is superlinear and subcritical. In [4] it was proved for peculiar f, the existence of a non-trivial C 2-solution of (1). The method is based upon an a-priori estimate and a fixed-point theorem in cones of Banach spaces. In this paper the nonlinearity is of a more general form, and we allow to the coefficients to go to zero at infinity in an arbitrary way and not necessarily exponentially. We use the notion of weight suitable to the integral operator associated to the Green function of L introduced in [5].
